Nineteen less than a number is 25 write the equation

Shtirlitz [24]

Answer:

Step-by-step explanation:

What this question is asking of you is what is the greatest common divisor of 12 and 15. Or, what is the biggest number that divides both 12 and 15.

in order to find this we have to split each number into it's prime components.

for 12 they are 2,2 and 3 (

2

⋅

2

⋅

3

=

12

)

and for 15 they are 3 and 5 (

3

⋅

5

=

15

)

Out of those two groups (2,2,3) and (3,5) the only thing in common is 3, so 3 is the greatest common divisor. That tells us that the greatest number of groups that can exist and have the same number of girls and the same number of boys for each group is 3.

Now to find out how many girls and boys there are going to be in each group we divide the totals by 3, so:

12

3

=

4

girls per group, and

15

3

=

5

boys per group.

(just as a thought exercise, if there were 16 boys, the divisors would have been (2,2,3) and (2,2,2,2), leaving us with 4 groups [

2

⋅

2

] of 3 girls [12/4] and 4 boys [16/4] )

8 0

3 years ago

Randy is walking home from school. According to the diagram above, what is his total distance from school to home? Show your wor

In-s [12.5K]

Answer:

First, when he walks, we can see in the image that between the school and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.

Then he needs to walk 2km.

Now if he has a jet-pack, he can ignore the buildings and just take the shorter path, here we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.

One of the catheti is the vertical distance (two blocks of 0.5km, so this catheti has a length of 2*0.5km = 1km), and the other one is the horizontal distance, also 1km.

The actual distance of this path is given by the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse, then:

H^2 = 1km^2 + 1km^2

H = (√2)km = 1.41km.

Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, in this case the distance and the displacement would be the same.

This is because the definitions of distance and displacement are:

Distance: "how much ground an object has covered"

Displacement: "Difference between the final position and the initial position"

When he walks, the distance is 2km and the displacement is 1.41km , but when he uses the jet pack, the distance is equal to the displacement, both are 1.41km.

7 0

4 years ago

PLEASE HELP ASAP 30 POINTS!!!

Helen [10]

Answer:

a=1, b=2, c=5, d=1, e=6

Step-by-step explanation:

$\frac{1}{2} \times (2x+4)(x+3)=(x+2)(x+3)=x^2+5x+6\\$

So $a=1, b=2, c=5, d=1, e=6$

7 0

3 years ago

In right ABC, AN is the altitude to the hypotenuse. FindBN, AN, and AC,if AB =2 5 in, and NC= 1 in.

Rama09 [41]

From the statement of the problem, we have:

• a right triangle △ABC,

,

• the altitude to the hypotenuse is denoted AN,

,

• AB = 2√5 in,

,

• NC = 1 in.

Using the data above, we draw the following diagram:

We must compute BN, AN and AC.

To solve this problem, we will use Pitagoras Theorem, which states that:

$h^2=a^2+b^2\text{.}$

Where h is the hypotenuse, a and b the sides of a right triangle.

(I) From the picture, we see that we have two sub right triangles:

1) △ANC with sides:

• h = AC,

,

• a = ,NC = 1,,

,

• b = NA.

2) △ANB with sides:

• h = ,AB = 2√5,,

,

• a = BN,

,

• b = NA,

Replacing the data of the triangles in Pitagoras, Theorem, we get the following equations:

$\begin{cases}AC^2=1^2+NA^2, \\ (2\sqrt[]{5})^2=BN^2+NA^2\text{.}\end{cases}\Rightarrow\begin{cases}NA^2=AC^2-1, \\ NA^2=20-BN^2\text{.}\end{cases}$

Equalling the last two equations, we have:

$\begin{gathered} AC^2-1=20-BN^2.^{} \\ AC^2=21-BN^2\text{.} \end{gathered}$

(II) To find the values of AC and BN we need another equation. We find that equation applying the Pigatoras Theorem to the sides of the bigger right triangle:

3) △ABC has sides:

• h = BC = ,BN + 1,,

,

• a = AC,

,

• b = ,AB = 2√5,,

Replacing these data in Pitagoras Theorem, we have:

$\begin{gathered} \mleft(BN+1\mright)^2=(2\sqrt[]{5})^2+AC^2 \\ (BN+1)^2=20+AC^2, \\ AC^2=(BN+1)^2-20. \end{gathered}$

Equalling the last equation to the one from (I), we have:

$\begin{gathered} 21-BN^2=(BN+1)^2-20, \\ 21-BN^2=BN^2+2BN+1-20 \\ 2BN^2+2BN-40=0, \\ BN^2+BN-20=0. \end{gathered}$

(III) Solving for BN the last quadratic equation, we get two values:

$\begin{gathered} BN=4, \\ BN=-5. \end{gathered}$

Because BN is a length, we must discard the negative value. So we have:

$BN=4.$

Replacing this value in the equation for AC, we get:

$\begin{gathered} AC^2=21-4^2, \\ AC^2=5, \\ AC=\sqrt[]{5}. \end{gathered}$

Finally, replacing the value of AC in the equation of NA, we get:

$\begin{gathered} NA^2=(\sqrt[]{5})^2-1, \\ NA^2=5-1, \\ NA=\sqrt[]{4}, \\ AN=NA=2. \end{gathered}$

Answers

The lengths of the sides are:

• BN = 4 in,

,

• AN = 2 in,

,

• AC = √5 in.

7 0

1 year ago

D = rt what does r stand for

AnnyKZ [126]

In the equation D = rt, the r stands for rate. The equation is saying that distance equals the rate at which you traveled multiplied with the time you traveled. In other words, r is the speed traveled. Example: If the rate at which you travel is 35 miles per hour and you traveled for 2 hours, then you have traveled 35 miles times 2 or 70 miles.

3 0

3 years ago